5 papers
Invasion Fronts in Shifting Habitats and Competition Systems: A Hamilton-Jacobi Approach and Nonlocal Effects
King-Yeung Lam, Chang-Hong Wu, Xiao Yu
We review recent developments in the study of spreading phenomena in reaction--diffusion equations arising from ecological invasion models. Motivated by the conjecture of Shigesada…
On the logarithmic correction of transition fronts in shifting environments
King-Yeung Lam, Chang-Hong Wu
In this paper, we investigate the location of the spreading front and convergence to traveling wave profile of solutions to the Fisher-KPP equation in the following two cases: (i)…
Asymptotic spreading of KPP reactive fronts in heterogeneous shifting environments II: Flux-limited solutions
King-Yeung Lam, Gregoire Nadin, Xiao Yu
We consider the spreading dynamics of the Fisher-KPP equation in a shifting environment, by analyzing the limit of the rate function of the solutions. For environments with a weak…
A Hamilton-Jacobi approach to road-field reaction-diffusion models
Christopher Henderson, King-Yeung Lam
We consider the road-field reaction-diffusion model introduced by Berestycki, Roquejoffre, and Rossi. By performing a "thin-front limit," we are able to deduce a Hamilton-Jacobi eq…
Asymptotic spreading of predator-prey populations in a shifting environment
King-Yeung Lam, Ray Lee
Inspired by recent studies associating shifting temperature conditions with changes in the efficiency of predator species in converting their prey to offspring, we propose a predat…